Introduction practice graphing problems in algebra:

Algebra deals with numbers and variables. Algebra is classified into pre- algebra, intermediate algebra and college algebra. It also deals with the concepts arising from terms, polynomials, expressions and algebraic equations. One of the methods of representing a set of objects is known as graph. In fact, an algebraic equation or quadratic equation can be represented geometrically by a line whose points make up the collection of solutions of the equation. If the students practice more algebra problems, then it will be easy for them to solve those problems. Practice makes perfect. 

 

 

Graphing algebra practice problem 1:

 

Solve the given equation and graph it, the equation is 3x + y – 15 = 0

Solution:

Write the given equation in slope intercept form,

y = mx + c

Adding 15 on both sides

3x + y – 15 + 15 = 0 + 15

3x + y = 15

Subtract 3x on both sides

3x – 3x + y = 15 – 3x

y = - 3x + 15

To find y- intercept, Put x = 0,

y = 0 +15

y = 15

To find x- intercept, put y = 0,

0 = - 3x + 15

Subtract 15 on both sides

-15 = - 3x + 15 – 15

-15 = - 3x

Divide 3 on both sides,

-15/3 = -3x/3

-5 = - x

x = 5

Now using this x and y intercept we can plot the graph, the coordinate points for graphing algebra problem are (5, 0) and (0, 15).

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Graphing algebra practice problem 2:

 

Find the solution of the system of equations.

y =x2 – 12

x +y =8

Solution:

Here the one equation is linear while the other equation is non linear

Plug first equation in equation two.

y = x2 – 12

x + (x2 – 12) = 8

x + x2 – 12 = 8

Subtract 8 on both sides

x + x2 – 12 – 8 = 8 – 8

x + x2 – 20 = 0

x2 + x – 20 = 0

On factoring it,

x2 + 5x – 4x – 20 = 0

(x2 + 5x) + (-4x - 20) = 0

Taking the common terms from the brackets

x(x + 5) – 4(x + 5) = 0

(x - 4) (x+5) = 0

The x coordinate points are 4, -5

Plug in the x values in first equation to get the y values

Plug in x = 4

y = (4)2 – 12

y = 16 – 12

y = 4

Now plug in the another x value, x = -5

y = (-5)2 – 12

y = 25 - 12

y = 13

The y coordinate points are 4,13

 

The coordinate points graphing algebra problem are (4, 4) (-5, 13) using these points graph can be plotted.

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